If , then wherever it is defined…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

If y=(a−x)a−x−(b−x)x−ba−x+x−by = \frac{(a-x)\sqrt{a-x} - (b-x)\sqrt{x-b}}{\sqrt{a-x} + \sqrt{x-b}}, then dydx\frac{dy}{dx} wherever it is defined is (a) x+(a+b)(a−x)(x−b)\frac{x + (a+b)}{\sqrt{(a-x)(x-b)}} (b) 2x−a−b2a−xx−b\frac{2x - a - b}{2\sqrt{a-x}\sqrt{x-b}} (c) −(a+b)2(a−x)(x−b)-\frac{(a+b)}{2\sqrt{(a-x)(x-b)}} (d) 2x+(a+b)2(a−x)(x−b)\frac{2x + (a+b)}{2\sqrt{(a-x)(x-b)}}

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